This paper attempts to detect non-linear patterns in daily nominal exchange rate returns of Indian rupee for a variety of bilateral currencies. The dual research strategy employed in this paper to detect non-linearity involves consideration of ARFIMA models for the data generating process of daily nominal exchange rate returns and 3 conventional non-linearity tests namely, McLeod Li test, Hinich test and BDS test for the daily nominal exchange rate return time series. The period of study spans over January 1983 to November 2000. The study finds significant non-linearities and long memory patterns in the daily data. The study also unearths some conflicting evidences of non-linearity by virtue of its dual research strategy.